There is no point in going any further if you are not permitted by law, or by landlord decree, to have a dog in your home or own your property. If your lease does not specify "no pets", and it wasn't agreed upon in the beginning of your time in the rental, approach your landlord about allowing you to have a dog. You may need actual, written consent from your landlord before you are able to buy or adopt a dog anyway, so it's important to do this right.
Pitching a Dog to Your Landlord
For more information on dogs in apartments and other rentals, please read:
The Apartment Dog
Locating Pet Friendly Rentals
Your Dog and Your Landlord
Breed Specific Legislation is a big hurdle to owning some dog breeds. These bans may be in effect at the state-level, or individually set by each city.
Check to see if your area has BSL in effect.
For more information on the laws and restrictions that might affect you and your dog-owning future, please read about the possible obstacles
in towns and neighborhoods, and
"Am I Allowed?".